Stat 11 Week 6
Experimenting with Probability
Prof. Suzy Thornton
Spring 2023
1. Data Introduction
We are going to use the laws of probability and properties of random variables to plan a trip. We will warm up by considering how conditional probabilities differ from marginal probabilities.
2. Analysis Goal
Ultimately, the goal of this analysis is the estimate the cost to fly several of us across the globe for a statistics conference. We will do this by using random variables to model the airline ticket prices of two different destinations.
Click this link to view the worksheet for experiments with random variables.
3. Summary of Results
It’s not easy to predict the outcome of a random phenomena but the mean and standard deviation are helpful in this regard.
Consider two independent random variables, \(X\) and \(Y\). Suppose the theoretical mean and standard deviation of \(X\) are \(E(X)\) and \(\sqrt{Var(X)}\), respectively. Suppose something similar holds for \(Y\). We can consider a new random variable \(W = X + Y\) and compute it’s theoretical mean and standard deviation using the fact that
\[E(W) = E(X) + E(Y), \quad\text{and } Var(W) = Var(X) + Var(Y).\]